I don't know how old you are, but if you're a teenager, my advice is to act the same way around girls you like as you do around your family and other people you're familiar with. Relax and say what you want to say. People can tell when someone is uptight or holding back a lot and relaxed people are much more popular. Being funny is a good way to start. I've found that people find it very funny when I open up and share my thoughts, and if you're funny, people will at the very least want to be around you. This will include girls you're attracted to. They will notice you before you notice them, which is ideal. Once you've made friends with a girl you're attracted to, keep opening up to her and if she opens up to you, you may have something going. I've never really had a girlfriend so I'm still figuring out how I can do the next step best. I also want to wait until I go to college, for several reasons.
The best thing to do is learn from experience. You'll know how good you are once you start doing it.
As for what to blurt out - make sure it is nothing gross, mean, sexual, etc. Make sure it is nothing nerdy either. Don't correct people, and compliment them once in a while. Don't tell the girl you like your feelings right away, instead give her opportunities to find that out on her own, and when she does, ask her out. Girls like being complimented, so telling a girl she is pretty is very good, but don't make it the first thing you tell her. Don't be overbearing, be a little bit underbearing, and if she is approaching you to talk to you, perfect.
Also, make sure the girl you like doesn't have a boyfriend or "thing" with some other guy.
Try not to hate me for telling you all of this, but 3-4 years ago I was in the same situation you were (very quiet around girls) and I grew out of it once I started being myself and stopped looking for advice on the internet. Even if James Bond wrote an advice column on how to pick up girls, it still wouldn't be perfect, because every guy and every girl is different and everyone is attracted to different people. Maybe if I knew you in real life or if you went into more detail, I could give you more specific advice. Everyone is unique and I'd say much more so even with AS people.
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"Psychic kids, try to understand who made them this way, so they don't feel bad...floating in space, the ghost is out there, so you're not alone, only out there"
Sagittarius, ISFP, diagnosed with AS when I was 13.
http://www.last.fm/user/DolphinCove